Mechanical impedance meter



July 23, 1935. P. B. FLANDERS MECHANICAL IMPEDANCE METER 2 Sheets-Sheet2 Filed April 4, 1933 /N V /V TOR P. FL ,4 NDERS A T TOR/VE Y Patented`luly 23, 1935 UNITED STATES PATENT i OFFICE Bell TelephoneLaboratories,

Incorporated,

New York, N. Y., a corporation of New York Application April 4, 1933,Serial No. 664,308

7 Claims.

The invention relates to the measurement of mechanical impedance andmore particularly to methods of and means for measuring the mechanicalimpedance of vibratory bodies at specied frequencies in a wide frequencyrange.

The principal object of the invention is a direct reading impedancemeter of high and uniform sensitivity over a Wide range of impedancesand l frequencies.

As described more in detail in Patent 1,880,425 granted to me, October4, 1932, a mechanical impedance may be regarded as the mechanicalanalogue of an electrical impedance. The impedance of a. mechanicalsystem may, therefore, be expressed in mechanical ohms (c. g. s. units)as the complex ratio of the force impressed on the sys tem to thevelocity produced in the system by that force, the force and thevelocity being the analogues respectively of the electromotive force andthe electric current.

According to the general features of the invention, the body or systemto be measured is coupled to a vibrating system having means forproducing directly voltages which vary respectively with theinstantaneous velocity of the system and 1the instantaneous forcerequired to drive the sys- In the preferred embodiment of the invention,the impedance to be measured is connected to a vibrating systemcomprising a coil and the moving electrode of a condenser transmitterand this system is elastically coupled to a tuned bar carrying the otherelectrode of the transmitter. The bar is vibrated electrostatically atthe test frequency and due to the elasticity of the coupling the movingsystem will vibrate with respect to the bar in a manner determined bythe nature and magnitude of its impedance. The voltage generated in -thecoil Will be proportional to its instantaneous velocity and the voltagegenerated by the condenser transmitter will vary with the displacementbetween the electrodes and hence with the force necessary to drive themoving system. These voltages are suitably amplified and balancedagainst each other through variable bridge elements which may becalibrated to read directly in mechanical ohms. Since this meterindicates the force and velocity directly, its sensitivity issubstantially uniform for a wide range of impedances and readings may betaken over a wide range of frequencies by merely varying the tuning ofthe bar and the frequency of the driving force.

The invention will be more clearly understood from the following detaildescription and the accompanying drawings in which:

Fig. 1 is a circuit diagram of an impedance meter according to thisinvention;

Fig. 2 is a detail view of the vibrating system;

Fig. 3 shows the vibrating bar;

Figs. 4 and 5 are assembly views of the tuned vibrating system; and

Fig. 6 is a sectional view and Fig. 7 an end view of the clamp operatingmeans.

Referring first to Fig. 2 the bar I I, which may be tuned to any desiredtest frequency as will be more fully described, is drilled and threadedat its free end to receive the duralumin diaphragms I2 and I3 which arerigidly coupled together at their centers by a bolt I4. This boltextends beyond the nut I5 to form a connection with the loudspeaker I8or other device whose impedance is to be measured. Clamped between thediaphragms is an annular insulator member I'I the face I8 of which isgold plated and spaced about 3 mils from the diaphragm I3 by a washer I9to form the electrode of the condenser transmitter. Secured to the lowerside of the diaphragm I3 is a phenol ber tubular piece 20 supporting, inthe gap 23, a coil 2I which is vibrated in the magnetic eld produced bythe winding 22.

The bar II is driven at any desired frequency by the oscillator 24 whichis connected between the bar and the driving plate 25 as shown. I'hisplate is cut away above the diaphragm I2 so that the electrostatic forceis exerted on the bar and the moving system is permitted to vibrate inaccordance with its own impedance. Since no polarizing voltage is usedin connection with the oscillator 24 the bar will vibrate at twice theoscillator frequency and the latter can be controlled accordingly toproduce the desired vibration of the bar. Polarizing voltage for thecondenser transmitter is applied between the electrode I8 and thediaphragm I3 by conductor 26 and since the variations in capacity in thecondenser transmitter are very small, it is essential to accuracy thatthere be no variation in the capacity between the conductor 26 and thebar II when the latter is vibrating. One convenient way of preventingthe conductor from vibrating is to mount the wire in the bore 2l andextend it through the opening 23 so that it can be tensioned in thecenter of the bore, One end of the bore is then sealed by a plug and asuitable powdered thermoplastic resin such as polystyrene is poured intothe open end and pressed down with a tubular plunger. When the bore isentirely lled the plunger is clamped in place and the bar is heated tofuse the material around the conductor. After cooling the plug andplunger are removed and the corroded material adjacent them is scrapedaway to insure high insulation resistance between the conductor and thebar. The conductor is then cut and attached to the terminal 29 of theelectrode 8.

The preferred mechanism for tuning the bar as shown in Figs. 4 to 7 isclaimed in a copending application of T. Aamodt, Serial No. 664,389,filed April 4, 1933. It consists essentially of clamps 30 with screws 3|for forcing the clamps into contact with the bar and jaw members 32having projections 33 engaging the clamps and means for turning the jawsabout the pivot 34 to force the clamps apart and progressively increasethe unclamped length of the bar. In the structure shown the clamp facesare flat but the faces of the bar are contoured to the deection curveso'f the clamps when they are under a suitably distributed load. Theradius of curvature, at any point along the face of such a bar istherefore greater than if the contours were those of a beam under thesame load concentrated at its free end. Hence with properly designedclamps a concentrated force applied to the ends of the clamps when theyare held in contact with the bar by screws 3| throughout their length,will first release only the ends of the clamps from the bar and as theconcentrated force is increased the free length of the bar isprogressively increased.

When the clamps are in contact with the bar over their entire length thebar resonates at its highest frequency and by spreading the jaws anydesired resonant frequency may be obtained over a wide range as forexample, from 11,000 to below 300 cycles per second. If higher or lowerfrequencies are required the bar may be proportioned accordingly andwhere necessary a series of interchangeable bars may be provided each ofwhich is capable of being tuned to a portion of the desired range. Thejaws may be conveniently operated by the mechanism shown in Fig. 6. Inthe rectangular cavity 35 in the base block 35, the block 31 is threadedto receive the machine screw 38 and is connected to the upper set ofjaws 32 by the straps 39 and the dowel pins 40. 'I'he end of the screw38 contacts the bottom of the member 4| which is connected to the lowerjaws 32 by dowel pins 42 and is adapted to move vertically between thestraps 39. When the screw 38 is forced against the member 4| the ends ofthe lower jaws are moved upwardly and at the same time the movement ofthe screw through the block 31 pulls downwardly on the straps 39 and theends of the upper jaws. With this arrangement the forces applied to theupper and lower jaws will be the same and since both sets are in contactwith the pivot 34 the other ends of the jaws will spread and force theclamps 30 apart by means of the projections 33. It will be noted thatthese projections are contoured as shown in Fig. 5 in such a way that asthe clamps are forced apart the force is always applied to the end ofthe clamp so that contact between the clamps and the bar is brokenprogressively along the clamp to progressively decrease its resonantfrequency.

In Fig. 1 the coil 2|, the condenser electrodes I3, I8 and theelectrostatic driving plate 25 are indicated schematically to show theirelectrical relation to the rest of the circuit. The coil is coupled tothe amplifier 43 by the transformer 44 and the output of the amplifieris impressed through transformer 45 on the terminals 46, 41 of thebridge. circuit 48. It will be understood that in practice the elementsof the bridge 48 must be suitably Shielded in accordance with well knownprinciples to localize the distributed capacities but in order to avoidunnecessary complication of thc drawings this shielding has not beenshown. The condenser transmitter is connected through amplifier 49,transformers 50, 5| and the equalizing network 52 to the terminals 53,54 of the bridge.

As stated in general terms above the procedure in using the bridge forimpedance measurements is to balance against each other the generatedvoltages the ratio of which is the niechanical impedance of the movingsystem. Under a condition of balance the settings of the bridge elementswill be a measure of the desired impedance but before the actualimpedance can be obtained the bridge must be calibrated and any phaseangle between the voltages e1 and e2 applied to the bridge which is dueto a difference in the transmission characteristics of the two channelsmust be eliminated.

Due to the use of transformers and multi-stage amplifiers thetransmission of these two channels will not be the same with respect toeither phase angle or amplitude but these differences may be correctedfor any single test frequency by means of the network 52. The variablecondensers 55, 56 in the bridge 48 are short circuited by theirrespective switches and switch 51 is closed in its lower position. Theoscillator 24 is set for the desired frequency and impresses analternating voltage on the resistors 58, 59, through the transformer 60.Switch 65 is closed cn contact 65 and switch 61 on contact 68 so thatthc voltage across resistor 58 is impressed on transformer 44 throughthe coil 2| and the voltage across resistor 59 is impressed on amplifier49 through the condenser transmitter since the conductor 69 is connectedto the bar which is in contact with the diaphragm |3 of the transmitter.'I'hese voltages are not necessarily of equal value but they must be inphase with each other. The resistance 6| is set for a value within theequalization limit and the resistor 62 and the inductance 63 of theequalizer 52 are adjusted until no sound is heard in the receiver 64.The channels are then equalized with respect to phase angle andmagnitude and the system is ready to be used for an impedancemeasurement at this particular frequency. The value of resistance 6|determines the magnitude of the constant (K) used in equations below forthe mechanical impedance measurements.

When the system is equalized and a mechanical impedance is to bemeasured the switch 51 is closed upwardly and the bar tuning mechanismalready described is adjusted to tune thc bar to the chosen frequency.The oscillator frequency is set to half that used for equalization sothat the bar will vibrate at the frequency for which the system wasequalized. The switch 65 is left closed on contact 66 since theresistance 58 is comparable to the impedance of the coil 2| but switch61 is closed on contact 10 since resistance 59 is negligible as comparedwith the impedance of the transmitter and by connecting the bar toground at 1| pick-up in the transmitter circuit from the oscillatordrive is prevented.

reactances condenser 55 may be used in which case switch I3 is open andswitch 12 is closed to short circuit condenser 56. For small negative orpositive reactances both condensers can be used, that is both switches'l2 and 'I3 may be open. 'For convenience in using the meter thevariable condensers 55 and 56 and the variable resistance 6I areprovided with direct reading dials. Assuming that the two channels areequalized yfor the particular test frequency being used and that thepotentialse1 and en are applied to the bridge as indicated in thedrawings, a balance is obtained by varying the condensers 55 and 5B andthe resistance 6I until the lower arms of the bridge have the properrelative impedance to produce a ditl'erence of potential between points53 and 54 due to the currents produced by voltage ve1 aloneV to balancevoltage e2. so that no current flows in the circuit of receiver 64. Forany given values of the elements in the lower arms of the bridge, thepotential between 53 and 54 will be directly proportional to e1 so thate2 is balanced against a voltage proportional to e1.

The equation for the mechanical impedance of the moving system in termsof the readings of the bridge elements is developed as follows:

(1) e1=KvV where V is the velocity of the coil 2| in cms. per sec. andKv is a constant the value of which will depend on the number of coilturns, the iiux density of the field and other factors.

(2) ez=KyI 9 F where Kf is a constant the value of which will depend onthe spacing of the condenser electrodes, the polarizing voltage used andother factors. F is the force in dynes applied to the moving system and9 represents the displacement in phase between this voltage and e1. Whenthe bridge circuit is balanced in the manner described above so that nosound is heard in the head receivers 64,

since R1 is very much greater than R,

1 1 0l' 1 wc wc,

i is substantially equal to i1+ia so that for practical purposes l "=2=added. By substituting for Zms in (10) 1 l jwzn=Znr,z (n) JKwc, +1 wma-JKwon ma=added mass in grams hence from which a 1 1 wm., wzrn,J (4)B2I1[R+J(;l)] (12) K-l- L and won wca ca c,

(s) e 1. R i e 1 so Zm=wm1 where ms is the effective mass of the l Rllmoving system and by substituting for K in (10) e 1 1 im 5mm (6)a=;[R-|J W CIVTC)] (13) ZM' JCL CXWC, 1% 1 7 2 Kf`|-"F l R+' 1. 1 f' ne,- K,V "R, J wel wc The procedure in taking impedance measurements of aparticular device such as the loudwhere speakerl is to connect it to themoving system KIUF of the bridge as shown in Fig. 2. 'I'he system is KI=K' then equalized for phase angle at the test fri- By properly adjustingthe resistance 82 and the mutual inductance 63 of the equalizer 52 thediierence in phase between e1 and e2 is eliminated so that for theequalized system Where Zm is the sum of the mechanical impedances of thedevice being measured and of the moving system of the impedance meterand which is the constant of the bridge as determined below.

To calibrate the bridge, that is, to determine the value of vK inEquation 8 and the impedance of the bridge alone, the bridge is iirstbalanced with no external impedance such as I6 attached to the screw I4and a second balance is obtained with a known mass attached to screw I4and with a suitable fixed setting of the resistance 6l. When theconstant is determined for this value of 6I it will hold for all latermeasurements when the ysame value of equalization resistance 6l is used.

In the case of the balance for the moving system without any externalimpedance wcs where Zms is the mechanical impedance of the moving systemof the impedance meter alone, K is the constant of the bridge as statedabove, and

wc, wel Wc c1 and c being the readings of the dials of the condensers 55and 56 when the bridge is balanced without any external impedance andfor the balance with the known added mass c1 and c being the readings ofthe condensers when the bridge is balanced with the known mass quency asdescribed above and a balance of ihe bridge 48 is then obtained. Thevalues of R, C1 and C are read from the dials associated mth frequencyused is then known and its value at any other frequency is obtained byrst equalizing for the other test frequency and obtaining a balance asbefore.

Since the impedance Equations (8) and (13) each involve "w terms(w=21rf) it will be seen that the bridge cannot be calibrated directlyin terms of the impedance of the vibrating systemv except for a. singlefrequency hence the foregoing substitution of values in the equations toobtain the desired impedance is necessary but since the resistance andcapacity values for the equations are read directly from the bridge, thecalculation required with this method is reduced to a minimum.

What is claimed is:

1. The method of measuring the mechanical impedance of a vibratorysystem which comprises vibrating the system, generating voltagesdirectly proportional respectively to the instantaneous velocity and theinstantaneous displacement of the system and balancing one of thevoltages against a. voltage proportional to the other voltage to obtaina complex ratio of the voltages in terms of known electrical impedances.

2. Apparatus for measuring mechanical impedance comprising a vibratingmember, means for driving the member. and means driven by the memberadapted to be connected to the impedance to be measured comprising meansfor measuring the instantaneous force applied to the impedance and othermeans for measuring the instantaneous velocity of the driven means.

3. In a mechanical impedance meter, a vibratable member and tuning meanstherefor, meansfor driving the member, a moving system adapted to beconnected to the impedance to be measured, an elastic coupling betweenthe system and the member, a condenser transmitter for gene/rating apotential proportional to the force applied to the system comprising anelectrode on the member and a. second electrode in the system,

an element in the system for generating a potential proportional to itsinstantaneous velocity, and means for comparing the phase angles andmagnitudes of the potentials.

4. Apparatus for measuring the mechanical impedance of a vibratingsystem comprising means for generating voltages directly proportionalrespectively to the instantaneous velocity and to the instantaneousdisplacement of the system, the ratio of which is the same proportion ofthe mechanical impedance to be measured at all frequencies, individualtransmission circuits for the voltages, means for equalizing thetransmission characteristics of the circuits, and means for comparingthe voltages transmitted.

5. In a mhanical impedance meter, a vibrating member, means for drivingthe member, driven means associated with said member adapted to beconnected to the impedance to be measured comprising means forgenerating a potential proportional to the instantaneous force appliedto the impedance, and other means for generating a potentialproportional to the instantaneous velocity of the driven means, ampliershaving their inputs associated with the generating means, means forequalizing the phase transmission characteristics of the amplifiers andvariable circuit elements for balancing the outputs of the amplifiers.

6. Apparatus for measuring mechanical impedance comprising a movingsystem including a coil and a metallic diaphragm rigidly connected tothe impedance to be measured, a tuned bar, means for driving the bar, anelastic coupling between the system and the bar, a polarized electrodemounted on the bar in operative relation to the diaphragm, means forproducing a magnetic field for the coil, and means for comparing thevoltages generated in the coil and between the electrode and thediaphragm. y

'1. In apparatus for measuring mechanical impedance. a bar xed at oneend, means for adjusting the resonant frequency of the bar, a movingsystem rigidly connected to the impedance to be measured comprisingtranslating devices generating voltages respectively proportional to thevelocity and the displacement of the system, an elastic coupling betweenthe system and the bar, and means for vibrating the bar at its resonantfrequency.

PAUL B. FLANDERS.

